Haitao Zou

About

I am a postdoc in the SFB-TRR 358 Integral Structures in Geometry and Representation Theory (project C8). I did my PhD at SCMS, Fudan University with Zhiyuan Li.

Galois representations of hyper-Kähler varieties

The Mumford–Tate conjecture, semisimplicity and purity of ℓ-adic cohomology, monodromy, and compatible systems of Weil–Deligne representations.

p-adic and characteristic p geometry

p-adic and crystalline cohomology, monodromy over p-adic fields, and the reduction of hyper-Kähler varieties: supersingularity and Frobenius splitting.

Moduli and finiteness

Shafarevich-type finiteness for hyper-Kähler and primitive symplectic varieties, their families and singularities, and the minimal model program.

News

Selected publications

All 5 publications

Unpolarized Shafarevich conjectures for hyper-Kähler varieties
Alg. Geom.

with Lie Fu, Zhiyuan Li, Teppei Takamatsu

Algebraic Geometry 13 (2026), 598–638

DOI arXiv PDF
Derived isogenies and isogenies for abelian surfaces
ANT

with Zhiyuan Li

Algebra & Number Theory 20 (2026), 1185–1234

DOI arXiv PDF HTML

Preprints

Semisimplicity, purity and Mumford–Tate conjecture for hyper-Kähler varieties

Preprint

with Kazuhiro Ito · 2026

arXiv PDF HTML BibTeX BibLaTeX

@misc{IZ26,
  author = {Ito, Kazuhiro and Zou, Haitao},
  title  = {Semisimplicity, purity and {Mumford--Tate} conjecture for hyper-{K{\"a}hler} varieties},
  year   = {2026},
  note   = {Preprint, arXiv:2610.07890 [math.AG]}
}

@online{IZ26,
  author      = {Ito, Kazuhiro and Zou, Haitao},
  title       = {Semisimplicity, purity and {Mumford--Tate} conjecture for hyper-{K{\"a}hler} varieties},
  date        = {2026},
  eprint      = {2610.07890},
  eprinttype  = {arxiv},
  eprintclass = {math.AG}
}

Quasi-$F$-split primitive symplectic varieties in positive characteristic

Preprint

2026

arXiv PDF HTML BibTeX BibLaTeX

@misc{Zou26,
  author = {Zou, Haitao},
  title  = {Quasi-{$F$}-split primitive symplectic varieties in positive characteristic},
  year   = {2026},
  note   = {Preprint, arXiv:2609.35467 [math.AG]}
}

@online{Zou26,
  author      = {Zou, Haitao},
  title       = {Quasi-{$F$}-split primitive symplectic varieties in positive characteristic},
  date        = {2026},
  eprint      = {2609.35467},
  eprinttype  = {arxiv},
  eprintclass = {math.AG}
}

Monodromy rank and the semisimple Mumford–Tate conjecture for hyper-Kähler varieties

Preprint

with Zhichao Tang · 2026 · submitted

arXiv PDF HTML BibTeX BibLaTeX

@misc{TZ26,
  author = {Tang, Zhichao and Zou, Haitao},
  title  = {Monodromy rank and the semisimple {Mumford--Tate} conjecture for hyper-{K{\"a}hler} varieties},
  year   = {2026},
  note   = {Preprint, arXiv:2602.19835 [math.AG]}
}

@online{TZ26,
  author      = {Tang, Zhichao and Zou, Haitao},
  title       = {Monodromy rank and the semisimple {Mumford--Tate} conjecture for hyper-{K{\"a}hler} varieties},
  date        = {2026},
  eprint      = {2602.19835},
  eprinttype  = {arxiv},
  eprintclass = {math.AG}
}

Arithmetic monodromy of hyper-Kähler varieties over $p$-adic fields

Preprint

with Kazuhiro Ito, Tetsushi Ito, Teruhisa Koshikawa, Teppei Takamatsu · 2025 · submitted

arXiv PDF HTML BibTeX BibLaTeX

@misc{IIKTZ25,
  author = {Ito, Kazuhiro and Ito, Tetsushi and Koshikawa, Teruhisa and Takamatsu, Teppei and Zou, Haitao},
  title  = {Arithmetic monodromy of hyper-{K{\"a}hler} varieties over {$p$}-adic fields},
  year   = {2025},
  note   = {Preprint, arXiv:2507.13713 [math.AG]}
}

@online{IIKTZ25,
  author      = {Ito, Kazuhiro and Ito, Tetsushi and Koshikawa, Teruhisa and Takamatsu, Teppei and Zou, Haitao},
  title       = {Arithmetic monodromy of hyper-{K{\"a}hler} varieties over {$p$}-adic fields},
  date        = {2025},
  eprint      = {2507.13713},
  eprinttype  = {arxiv},
  eprintclass = {math.AG}
}

In preparation

$\mathbb{Q}$-factorial simultaneous terminalizations for families of primitive symplectic varieties

with Chen Jiang, Zhiyuan Li

Draft ready · updated July 2026

Abstract

We prove that every $\mathbb{Q}$-factorial projective locally trivial family of primitive symplectic varieties admits a $\mathbb{Q}$-factorial simultaneous terminalization after a finite base change. Over a smooth complex curve, such a terminalization can be obtained after a finite etale base change whose degree is bounded in terms of the number of crepant divisors in a single fiber. Over an arbitrary reduced base, a finite surjective base change suffices; when the base is normal, the cover may be chosen etale. The proof uses finite monodromy of crepant divisors, relative extraction, polarized deformation, and a curve-completion argument via the minimal model program. As an application, we extend the pointed Shafarevich finiteness theorem to primitive symplectic varieties that are not necessarily terminal.

Haitao Zou

About

Galois representations of hyper-Kähler varieties

p-adic and characteristic p geometry

Moduli and finiteness

News

Selected publications

Unpolarized Shafarevich conjectures for hyper-Kähler varieties

Derived isogenies and isogenies for abelian surfaces

Preprints

Semisimplicity, purity and Mumford–Tate conjecture for hyper-Kähler varieties

Quasi-$F$-split primitive symplectic varieties in positive characteristic

Monodromy rank and the semisimple Mumford–Tate conjecture for hyper-Kähler varieties

Arithmetic monodromy of hyper-Kähler varieties over $p$-adic fields

In preparation

$\mathbb{Q}$-factorial simultaneous terminalizations for families of primitive symplectic varieties